Using statistical thinking and summarizing data

The peak of the data is not centered, and the body mass values fall off more sharply on the left of the peak than on the right. Numerical descriptors include mean and standard deviation for continuous data types like incomewhile frequency and percentage are more useful in terms of describing categorical data like race.

The infant was alternately shown these two scenarios several times. But then we have a similar question—could any differences we observe in the groups be an artifact of that group-formation process? In most statistical analyses you will use sample standard deviation and so n So where does this leave us with regard to the coffee study mentioned at the beginning of this module?

Descriptive statistics

A major problem lies in determining the extent that the sample chosen is actually representative. The Hawthorne effect refers to finding that an outcome in this case, worker productivity changed due to observation itself.

In the business world, descriptive statistics provides a useful summary of many types of data.


Each one is a slightly different measure of what happened "on average" in the experiment. The lower quartile corresponds to the item that has rank 0.

The results of studies with widely representative samples are more likely to generalize to the population. These summaries may either form the basis of the initial description of the data as part of a more extensive statistical analysis, or they may be sufficient in and of themselves for a particular investigation.

A data set with two modes is sometimes called "bimodal. Random sampling is paramount to generalizing results from our sample to a larger population, and random assignment is key to drawing cause-and-effect conclusions. It is entirely possible for a group of data to have no mode at all, or for it to have more than one mode.

The probability distribution of the statistic, though, may have unknown parameters. What graphs are relevant, and what do they reveal? So if we tossed a coin 16 times, could it land heads 14 times? Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically, sometimes they are grouped together as categorical variableswhereas ratio and interval measurements are grouped together as quantitative variableswhich can be either discrete or continuousdue to their numerical nature.

Because this p-value of 0. The replication is simply how many items there are in your sample that is, the number of observations. This probability is referred to as a p-value. Describe the role of p-values and confidence intervals in statistical inference.

Addressing the research question of whether the cancer pamphlets are written at appropriate levels for the cancer patients requires comparing the two distributions. The following illustration shows the mean, median, and mode of the "without compost" data sample on a graph.

You can think of it as a sort of "average deviation" from the mean. It is entirely possible for a group of data to have no mode at all, or for it to have more than one mode. For example, in the coffee study, did the proportions differ when we compared the smokers to the non-smokers?

This still leaves the question of how to obtain estimators in a given situation and carry the computation, several methods have been proposed: For example, imagine that you conducted a survey on the most effective way to quit smoking.

Yet comparing only the means of the two groups fails to consider the variability of creativity scores in the groups. At this stage of the project, the team felt that they did not understand much of the variation and, instead of continuing to employ the conventional DMAIC methodology, elected to implement a DOE.

In addition, readability level was determined for a sample of 30 pamphlets, based on characteristics such as the lengths of words and sentences in the pamphlet.

Statistical Thinking

It says nothing about how the data are distributed between those two endpoints. These 5 values split the data sample into four parts, which is why they are called quartiles. There is no single central tendency.

Performing the experiment following the experimental protocol and analyzing the data following the experimental protocol.

Tables are a useful way of describing both qualitative and grouped quantitative data and there are also many types of graph that provide a convenient summary. The mean, however, would now be 5.

The mean 5 is the arithmetic average of all the data points. The team first mapped the network to gain an understanding of the process flow then used the conventional DMAIC methodology.

Yes, because of the random assignment used in the study. Performing the experiment following the experimental protocol and analyzing the data following the experimental protocol. These two variables reveal two fundamental aspects of statistical thinking:Learn how to analyze data using one of the most powerful statistical software packages available: MATLAB MATLAB is a highly useful tool for complex computation as it allows high-order calculations and analysis in matrices.

Statistics review 1: Presenting and summarising data

Summarizing and Exploring Data Summarizing univariate data: numerically (sample mean, IQR, etc.) and by plotting (pie/bar/pareto chart for categorical data, histogram, box plot, normal plot) Summarizing bivariate data: Simpson's paradox, scatter plot, sample correlation coefficient.

Watch video · The course covers important statistical terms and definitions, and then dives into techniques using the tools in Excel: formulas and functions for calculating averages and standard deviations, charts and graphs for summarizing data, and the Analysis ToolPak add-in for even greater insights into data.

Statistics, Data, and Statistical Thinking. Statistical thinking. Involves applying rational thought to assess data and the inferences made from them critically. be found using formula, for grouped data Or where score is repeated [like formula for median] Percentile Rank. 1 Chapter 1 Statistics, data and statistical thinking.

The science of Statistics. Statistics. is the science of_____. It involves collecting, classifying, summarizing. Statistics – A guide.

These pages are aimed at helping you learn about statistics. Why you need them, what they can do for you, which routines are suitable for your purposes and how to carry out a range of statistical analyses.

On this page: Summarizing data.

Using statistical thinking and summarizing data
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